Question: $f(x)=\dfrac{3}{1-{{x}^{2}}}$ Find a power series for $f$. Choose 1 answer: Choose 1 answer: (Choice A) A $3+3x+\text{ }\ldots +\text{ }3{{ x }^{n}}+\ldots$ (Choice B) B $3x+3{{x}^{2}}+...+3{{x}^{n+1}}+\ldots$ (Choice C) C $3\text{ }+\text{ }3{{x}^{2}}\ldots +\text{ }3x^{2n}+\ldots$ (Choice D) D $3\text{ }+\text{ }9{{x}^{2}}+\ldots +\text{ }{{\left( {{3x}^{2}} \right)}^{n}}+\ldots$
This is a geometric series with first term $a\text{ }=\text{ }3$ and common ratio $r\text{ }=\text{ }{{x}^{2}}$. Therefore, the series is as follows: $3\text{ }+\text{ }3{{x}^{2}}+\text{ }3{{x}^{4}}+\text{ }3{{x}^{6}}+\ldots +\text{ }3(x^{2})^{n}+\ldots $